Going to need a little more info. Do the apps randomly appear in the apps drawer or on one of the home screens?

If appearing on the home screen, there is probably a rogue app putting shortcuts there and deleting them just moves the shortcut to the trash, not the app itself. If this is the case, you're going to have to uninstall each app in reverse order they were installed (uninstall most recently installed first) until you find out which app is the culprit. I think there might also be an app that will find rogue apps on your device, but I can't think of the name of it at the moment.

If appearing in the apps drawer, then I'm not aware of any way for this to happen other than the user actually installing apps.